Explain how you know if a radical expression is in simplest form..
A radical expression is in simplest form when the radicand (the number under the square root symbol) cannot be simplified further. This means that the radicand is not a perfect square and cannot be factored into a product of a perfect square and another number.
To determine if a radical expression is in simplest form, you can check if the number under the radical sign can be simplified further by factoring out perfect squares from it. If there are no perfect squares that can be factored out from the radicand, then the radical expression is in simplest form. Additionally, the radical sign should not have any fractions or variables under it, and the index (the number outside the radical sign) should be the smallest possible integer for that expression.
use simpler terms
A radical expression is in simplest form when the number under the square root sign cannot be simplified any further further. It means that you can't take the square root of the number under the radical again or simplify
How can you tell if radicals are like radicals?
Radicals are considered like radicals if they have the same index and the same radicand.
For example, √2 and √2 are like radicals because they both have the same index (2) and the same radicand (2). Similarly, ³√5 and ³√5 are like radicals as they have the same index (3) and the same radicand (5).
However, radicals are not like radicals if they have different indices or different radicands. For instance, √2 and ³√2 are not like radicals as they have different indices (2 and 3) even though they have the same radicand (2). Similarly, √3 and √5 are not like radicals as they have the same index (2) but different radicands (3 and 5).